\newproblem{lay:5_1_4}{
  % Problem identification
	\begin{large}
	  \hspace{\fill}\newline
    \textbf{Lay, 5.1.4}
	\end{large}
	\\
  \ifthenelse{\boolean{identifyAuthor}}{\textit{Ana Pe\~na Gil, Jan. 19th 2014} \\}{}

  % Problem statement
	Is $\begin{pmatrix}-1\\1\end{pmatrix}$ an eigenvector of $\begin{pmatrix}5 & 2 \\ 3 & 6\end{pmatrix}$?
	If so, find its eigenvalue.
}{
   % Solution
	To check whether $\begin{pmatrix}-1\\1\end{pmatrix}$ is an eigenvector or not, we test whether it has the property
	\begin{center}
		$\begin{array}{rcl}
		   A\mathbf{v}&=&\lambda\mathbf{v}\\
			 \begin{pmatrix}5 & 2 \\ 3 & 6\end{pmatrix}\begin{pmatrix}-1\\1\end{pmatrix}&=&\begin{pmatrix}-3\\3\end{pmatrix}=3\begin{pmatrix}-1\\1\end{pmatrix}\\
		\end{array}$
	\end{center}
	So, $\begin{pmatrix}-1\\1\end{pmatrix}$ is an eigenvector and its associated eigenvalue is $3$.\\
}
\useproblem{lay:5_1_4}
\ifthenelse{\boolean{eachProblemInOnePage}}{\newpage}{}
